reserve x,y,z,c for object,
  f for Function of 2-tuples_on BOOLEAN, BOOLEAN;

theorem
  [<*x,y*>,f] in the carrier of 2GatesCircStr(x,y,c,f) & [<*[<*x,y*>,f],
  c*>, f] in the carrier of 2GatesCircStr(x,y,c,f)
proof
  set S1 = 1GateCircStr(<*x,y*>, f);
  set S2 = 1GateCircStr(<*[<*x,y*>, f], c*>, f);
  [<*x,y*>, f] in the carrier of S1 & [<*[<*x,y*>,f], c*>, f] in the
  carrier of S2 by Th43;
  hence thesis by Th20;
end;
